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A Note on Costs Minimization with Stochastic Target Constraints
Yan Dolinsky, Benjamin Gottesman, Ori Gurel-Gurevich · 2019-07-04 · via math.PR updates on arXiv.org

We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order semi--linear ordinary differential equation (ODE). Moreover, we establish the optimal control. In the second example we show that the case of exponential costs leads to a trivial optimal control.

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